Welcome aboard. This shouldn't be too tough to isolate where the problem is coming from and handle it. First need to figure out if this is related to fuel, electrical or your transmission. Fuel is the simple place to start. With the boat in the water and the doghouse open and the flame arrestor removed, you need to carefully inspect what is happening in the carb as it stalls and is hard to restart. You need to see that the choke blade is open all the way. You also need to determine if the carb is getting too much fuel and flooding out, or not getting enough fuel and running out of gas. After it stalls, watch to see if there is any fuel being squirted by the accelerator pump.
You can monitor spark at a spark plug wire or the coil wire with a timing light. Simply use duct tape to keep the trigger in and have someone watch to see what the light does in relationship to the engine.
Another possibility is a transmission/drive-shaft issue. If it is binding, it may not allow you to operate the boat. What does the fluid look and smell like? Is the level correct? Visually inspect the running gear under the boat for any damage.
Whew.......that should keep you busy for a bit. Hopefully not too busy to post a pic of this boat. We all love to see boat pics.
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